Rényi 提纯纠缠是非加性的

中文摘要 AI 辅助

提纯纠缠是一种衡量总关联的基础物理量，其加性问题尚未解决。我们针对两量子比特经典态在不同 Rényi 阶下研究该量的加性。对于所有 α∈[0,1)，我们在该态族内证明了非加性，其证据是单个态的两份拷贝。我们首先精确求解了该族在每个 Rényi 阶下的单拷贝优化问题。随后，我们将两拷贝优化限制在一组自然的有限纯化集合中，并展示了其中一个纯化的熵严格低于乘积值。相比之下，对于 α∈[2,∞]，我们在该族内证明了张量积下的加性。α∈[1,2) 区间（包括 von Neumann 情形 α=1）仍未解决，我们推测在整个该族内均存在加性。

英文摘要

Entanglement of purification is a fundamental measure of total correlations whose additivity remains unresolved. We study its additivity for classical states on two qubits at different Rényi orders. For every $α\in[0,1)$, we prove nonadditivity within this family, witnessed by two copies of a single state. We first solve the one-copy optimization exactly for the entire family at every Rényi order. We then restrict the two-copy optimization to a natural finite set of purifications and exhibit one whose entropy is strictly below the product value. In contrast, for $α\in[2,\infty]$ we prove additivity under tensor products within this family. The interval $α\in[1,2)$, including the von Neumann case $α=1$, remains open, and we conjecture additivity there throughout the same family.

发表机构

• University of Waterloo（滑铁卢大学）
• Institute for Quantum Computing, University of Waterloo（滑铁卢大学量子计算研究所）
• Perimeter Institute for Theoretical Physics（理论物理珀蒂默研究所）

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